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Beliebt Rechnen >

inverselaplace ((s+2))/(s(s+4))

Lösung

inverse laplace transformation

\frac{( s + 2 )}{s ( s + 4 )}

Lösung

\frac{1}{2} H (t) + \frac{1}{2} e^{- 4 t}

Schritte zur Lösung

L^{- 1} {\frac{( s + 2 )}{s ( s + 4 )}}

Ermittle den Partialbruch von

\frac{s + 2}{s ( s + 4 )} : \frac{1}{2 s} + \frac{1}{2 ( s + 4 )}

= L^{- 1} {\frac{1}{2 s} + \frac{1}{2 ( s + 4 )}}

Wende die lineare Eigenschaftder inversen Laplace-Transformation an:

Für Funktionen

f (s), g (s)

und Konstanten

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= L^{- 1} {\frac{1}{2 s}} + L^{- 1} {\frac{1}{2 ( s + 4 )}}

L^{- 1} {\frac{1}{2 s}} : \frac{1}{2} H (t)

L^{- 1} {\frac{1}{2 ( s + 4 )}} : \frac{1}{2} e^{- 4 t}

= \frac{1}{2} H (t) + \frac{1}{2} e^{- 4 t}

Beliebte Beispiele

derivative of tan(5x+5)

\frac{d}{d x} (tan (5 x + 5))

integral from 0 to 3 of x/(sqrt(9-x^2))

\int_{0}^{3} \frac{x}{9 - x ^{2}} d x

integral of 45sqrt(t)-(21)/(sqrt(t))

\int 45 t - \frac{21}{t} d t

derivative of 2/(x^3+1)

\frac{d}{d x} (\frac{2}{x ^{3} + 1})

derivative of (-5/(x^5))

\frac{d}{d x} (\frac{- 5}{x ^{5}})